There is no largest number. As others have said Graham’s number is incomprehensibly large. There just isn’t any real intuitive way to make sense of its scale. It’s notable because it was for some time the largest number used in a serious mathematical proof. It has since been supplanted by some other ridiculously large numbers.
It gained notoriety because of its largest in a proof status, but also because of the fact that just explaining how to construct it to a layman was very difficult to do. It requires repeated iteration of a type of mathematical operation that is not something non-mathematicians would learn. Once you begin to understand how those operations work, and explore the process of forming the number, you start to see that even after one or two of the first iterations you’ve already constructed an enormously large value, and that’s only the beginning.
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